This is a large, multi-center, randomized, double-blind, placebo-controlled study to evaluate the safety, tolerance, and effectiveness of each of the three treatment arms. Six hundred children between 3 months and 18 years will be enrolled. Children who have received less than 6 weeks of AZT or similar therapy are eligible. If children develop toxicity and are on either AZT alone or ddI alone, they may "cross over" to the other single-arm of therapy. The study includes frequent evaluations to see if one arm of treatment is better than others